Seismic diffracted waves from topography using 3-D discrete wavenumber‐boundary integral equation simulation

Compressional (P) and shear (S) wave diffraction by free‐surface topography plays a prominent part in the prediction of site responses for seismic risk estimation. Wave propagation modeling in 3-D media is required for an accurate estimation of these diffractions. We have extended the discrete wavenumber‐indirect boundary integral equation method for a 3-D geometry in the case of irregular topography. The Green’s functions are expressed as finite sums of analytical density functions over the horizontal wavenumbers using the spatial periodicity of the topography and a discretization of the surface. We show that the evaluation over vertical wavenumber kz of the analytical integral is possible because a new factor in 1/k2 exists. When the force point and the receiver point are at the same vertical position, we develop a numerical strategy to choose the sign of the exponential factor, which is not given by the analytical formulation. The free‐stress boundary conditions at the topography lead to a large linear...